Question

During the last semester, 60 students of Planning and Public Policy Program (PPPP) at Rutgers University took the Basic Statistics course. Twelve of these students received more than 80 for the final exam. At 99% level of confidence, estimate the percentage of all students of PPPP who received more than 80 for the final exam of the Basic Statistics course during the last 10 years.

A. 7% to 33%

B. 18% to 22%

C. 59%

D. None of the above.

Answer 1

Option (A) 7% to 33%

Explanation:

Data provided in the question:

Total number of students , n = 60

Number of students received more than 80 = 12

Probability of number of students received more than 80, p =
`(12)/(60)` = 0.2

Confidence level = 99%

Now,

percentage of all students of PPPP who received more than 80 for the final exam of the Basic Statistics

⇒ p ±
`z*\sqrt{(p(1-p))/(n)}`

here,

z = 2.58 for 99% confidence level

Thus,

⇒ 0.2 ±
`2.58*\sqrt{(0.2(1-0.2))/(60)}`

or

⇒ 0.2 ± 0.13

or

⇒ ( 0.2 - 0.13 ) to ( 0.2 + 0.13 )

or

⇒ 0.07 to 0.33

or

⇒ 7% to 33%

Hence,

Option (A) 7% to 33%